is the logical OR function. It evaluates its arguments in order, giving True immediately if any of them are True, and False if they are all False.


  • Or[e1,e2,] can be input in StandardForm and InputForm as e_(1)∨e_(2)∨.... The character ∨ can be entered as ||, or, or \[Or].
  • Or has attribute HoldAll, and explicitly controls the evaluation of its arguments. In e_(1)||e_(2)||... the e_(i) are evaluated in order, stopping if any of them are found to be True.
  • Or gives symbolic results when necessary, removing initial arguments that are False.


open allclose all

Basic Examples  (4)

Combine assertions with ||:

A symbolic disjunction:

A system of equations:

Enter using or:

Scope  (5)

Or works with any number of arguments:

Or is associative:

Or with explicit True or False arguments will simplify:

Or evaluates its arguments in order, stopping when an argument evaluates to True:

The order of arguments may be important:

Symbolic transformations will not preserve argument ordering:

TraditionalForm formatting:

Applications  (6)

Combine conditions in a Wolfram Language program:

If an argument of Or evaluates to True, any subsequent arguments are not evaluated:

The argument order in Or matters; if the last two arguments are reversed, I0 is evaluated:

Combine assumptions:

Combine equations and inequalities; Or is used both in the input and the output:

Use || to combine conditions:

A cellular automaton based on Or:

Find the area of the union of sets given by algebraic conditions:

This shows the set:

Properties & Relations  (7)

Truth table for binary Or:

Ternary Or:

Zero-argument Or is False:

Or with a single argument will return the evaluated argument regardless of value:

&& has higher precedence than ||:

Use BooleanConvert to expand And with respect to Or:

De Morgan's laws relate And, Or, and Not:

Disjunction of conditions corresponds to the Max of Boole functions:

Introduced in 1988
Updated in 1996